Finite Group DatabasebetaFinite Group DatabasebetaOrder 2176.
596 conjugacy classes of subgroups; only the 165 normal subgroups are shown.
This group has 596 conjugacy classes of subgroups — too many to draw. Only its 165 normal subgroups are shown.
Dotted edges: containments with no intermediate normal subgroup — omitted non-normal subgroups may lie between.
Splittings G = N ⋊ H with N normal; H ≅ G/N.
| N | H ≅ G/N | type |
|---|---|---|
| 2. #11762735 | C2 | semidirect |
| 3. #11762710 | C2 | semidirect |
| 4. #11762688 | C2 | semidirect |
| 5. #11762674 | C2 | semidirect |
| 6. C4×C22⋊Dic17 | C2 | semidirect |
| 7. C22×C4⋊C4×C17 | C2 | semidirect |
| 88. C22×C4⋊C4 | D17 | semidirect |
| 115. C17 | #2504 | semidirect |
By isomorphism type — maximal subgroups of the same type appear once, whether or not they are normal.
| subgroup | index |
|---|---|
| C2×#10587616 | 2 |
| #11762735 | 2 |
| #11762710 | 2 |
| #11762688 | 2 |
| #11762674 | 2 |
| C4×C22⋊Dic17 | 2 |
| C22×C4⋊C4×C17 | 2 |
| #2504 | 17 |